Final answer:
The population in Hardy-Weinberg equilibrium demonstrates random mating and no immigration or emigration, but no constant rate of mutation. The correct answer is I and II, aligning with Hardy-Weinberg conditions except for the absence of mutations.
Step-by-step explanation:
The student's question is about which conditions apply to a population in Hardy-Weinberg equilibrium. The Hardy-Weinberg principle outlines five conditions for a population to maintain this equilibrium: no mutations, no gene flow (no immigration or emigration), a very large population size, random mating, and no natural selection. The possible truths about the population in question are: random mating (I), no immigration or emigration (II), and a constant rate of mutation (III).
The correct answer to the question is that only conditions I (random mating) and II (no immigration or emigration) are true. A constant rate of mutation is in conflict with the Hardy-Weinberg assumption of no mutation, so condition III is not applicable. Therefore, the population in Hardy-Weinberg equilibrium must exhibit random mating and be isolated, with no immigration or emigration, but does not have a constant rate of mutation.
Answer: b. I and II